Teaching

Homogenization of Partial Differential Equations (WS2023/2024))

Time/Room: tba

Hours per week: 4

Language: English


In this lecture we deal with mathematical methods of multi-scale analysis for the treatment of problems in heterogeneous media. Starting from a microscopic model which describes the heterogeneous structure (and the physical processes) using oscillatory coefficients or geometry, the goal is to derive macroscopic models with homogenized/effective coefficients that provide an approximation of the microscopic model. For this purpose, we use rigorous techniques such as two-scale convergence, where we restrict ourselves to periodic problems. As applications, we will consider the diffusion equation and Darcy's law. The latter can be derived from the Stokes equation in (periodically) perforated domains by means of homogenization.


Prerequisites: Analysis 1-3, Functional Analysis, Sobolev spaces and weak theory for elliptic (stationary) PDEs


Previous teaching

Winter term 2024/2025: Zeitabhängige partielle Differentialgleichungen

Summer term 2024: Mathematische Methoden in der Strömungsmechanik

Winter term 2023/2024: Höhere Analysis (Analysis 3)

Summer term 2023: 

Summer term 2021: Introduction to multi-scale analysis and homogenization

Summer term 2020: Mathematische Methoden in der Strömungsmechanik

Summer term 2018: Nichtlineare Analysis